CBSE BoardEnglish MediumSTD 10MathsArithmetic Progressions3 Marks
Question
Write the first three terms of the APs when a and d are as given below: $\text{a}=\sqrt{2},\text{d}=\frac{1}{\sqrt{2}}.$
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Answer
Given that, first term $\big(\text{a}\big)=\sqrt{2}$ and common difference $\big(\text{d}\big)=\frac{1}{\sqrt{2}}$
$\because$ $n^{th}$ term of an AP, $T_n = a + (n - 1)d$
$\therefore$ second term of an AP, $T_2 = a + d$
$\text{T}_{2}=\sqrt{2}+\frac{1}{\sqrt{2}}=\frac{2+1}{\sqrt{2}}$
$\text{T}_{2}=\frac{3}{\sqrt{2}}$
and third term of an AP, $T_3 = a + 2d$
$\text{T}_{3}=\sqrt{2}+\frac{2}{\sqrt{2}}=\frac{2+2}{\sqrt{2}}$
$\text{T}_{3}=\frac{4}{\sqrt{2}}$
Hence, requied three term are $\sqrt{2},\frac{3}{\sqrt{2}},\frac{4}{\sqrt{2}}.$
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